Theorem 9 [1]}
Suppose that \(q \ge 1 .\)  Let \(\mathcal {G}\)  and \(\mathcal {K}\)  be real mappings on \([m_1, m_2]\) . If \(|\mathcal {G}|\)  and \(|\mathcal {G}||\mathcal {K}|^{q}\)  are integrable functions in the given interval, then
\(\int _{m_1}^{m_2}|\mathcal {G}(x) \mathcal {K}(x)| d x \le \left(\int _{m_1}^{m_2}|\mathcal {G}(x)| d x\right)^{1-\frac{1}{q}}\left(\int _{m_1}^{m_2}|\mathcal {G}(x)||\mathcal {K}(x)|^{q} d x\right)^{\frac{1}{q}}\) 
